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GCSE Maths exam question help!!


ShutkiRepublic
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Hi there, i was doing a paper, and i came across a question, i have tried it, but i don't know where to start from ;(

Please help me!

I have attached the question down below.

mathq

 

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Zeeshan Ahmed
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To answer this question, I would do the following

1. Find out the area of the small hexagon in terms of x. To do this, basically make triangles from the centre of the hexagon, to each vertex. Then, work out the area of one of the triangles using 1/2 x base x height and times it by how many triangles were in the hexagon. [Note: to work out the area of the small triangle, you're gonna need to do SOH CAH TOA].

image

2. Once you got the area of the small hexagon in terms of x, times it by p^2 to get the area of the large hexagon. (Remember, if the length scale factor is p, the area scale factor is p^2). Once you times it by p^2, take away your two areas and factorise - you'll end up with what they've given you.

Spoiler
My solution, look at it after trying it yourself
image
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ShutkiRepublic
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@zeeshan Thanks so much for the response, i have another question to ask, but I can't upload the question onto here. Do you have any email or social media? Its very urgent.

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Zeeshan Ahmed
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@shutkirepublic

Unfortunately I can only reply to questions on this forum

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ShutkiRepublic
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@zeeshan Oh ok, i have a few more questions that i am stuck with, is it ok if you can help me?

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ShutkiRepublic
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These are the questions.

Thanks 😀

image

 

image

 

image

 

image

 

 

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Zeeshan Ahmed
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@shutkirepublic

This is how you should approach these ratio questions. Make x or y the subject of the equation they’ve given you, then plug in a value for x and y. Have a look at the example below 

650BEC71 C712 4D4A AAC6 39411342401E

if you have a quadratic and it says make a ratio from it, make one side equal 0, factorise it, make each bracket = 0 and do the same thing as above. 

Spoiler
Solution to the part (b) if you’re still stuck

E51D9EB9 0AD6 46C5 8BFC 80BF4A95CC30

For the circle theorem question, use the alternate segment theorem. The angle x is equal to the angle I put an arrow next to. Try to work out that angle using the theorems you know, then x is the same thing.

For the mean question, approach it like the following:

FD813424 A3D4 4E06 A50F 06E2E9F9DA93

 

For the lower bound question, break it down using other triangles in the cube:

0D275E8F B95A 4373 857D B3391027CB31
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Hafsa
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@zeeshan Hi I was looking through your working out for the ratio solving question (part b), and I noticed that there might have been a mistake. 

image

3x would have to multiply with 2x to get 6x^2 and that would change the answer at the end, although I'm not sure if I am correct.

Here is my attempt to go further but I got 2 y values and now I'm confused... :/

image

Thanks

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Zeeshan Ahmed
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@hafsa

Yes, your factorisation is correct. (2x - 5y)(3x + 4y)

The reason you didnt get a negative value was just a small mistake right at the end

When you make y the subject, you wouldve divided both sides by -4, so y = -3/4. 

Well done though!

Just out of curiosity, how did you find this thread?

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Hafsa
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@zeeshan Ohh, yeah I get the question now, thanks. So would the end ratio at the end be 

x:y

3:2

[since the y fraction would be 2/5]

And I got this question from one of my previous tests, and I was confused about this one so I found this thread online. 

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Zeeshan Ahmed
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@hafsa

When you let x = 1, y = 2/5

So x : y is 1 : 2/5

or if you times both sides, then x : y = 5 : 2

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Hafsa
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@zeeshan Oh yes I completely ignored the x value

Thanks I get it now 🙂

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Zeeshan Ahmed
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@hafsa

No problem ? 

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mathsflyinginsectbee
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@zeeshan 

could you help me with this question please 

image
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Zeeshan Ahmed
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@mathsflyinginsectbee

Part a, the new triangles should look like this

 

8E452D64 60AA 4768 B0F6 9ACC86C3C047

 

for the “single transformation”, I would say it’s a reflection by a scale factor of -1, from centre point (2.5, -1)

 

0CCE9E90 9FA2 469F AA1C 1CBBE8ECF36A

 

for part b, an invariant point is a point that doesn’t change after the transformation, the only point that would stay the same after an enlargement with scale factor -1 at the point (2.5, -1) is the point (2.5, -1).

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mathsflyinginsectbee
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@zeeshan sorry to bother you but would you be able to further explain the answer to the cube question please

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Zeeshan Ahmed
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@mathsflyinginsectbee

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Elizabeth
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@zeeshan hi, would you know what topic this would fall under? so i could practise it. thanks.

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sisif
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Hi, by any chance do you know what the paper is called? i did this for my test and was curious about other questions but don’t have it online to share! 

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Zeeshan Ahmed
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@sisif

Unfortunately I got no idea where these papers are from ?

If someone knows, that would be nice though. Seems like some hard questions were in the paper.

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AMG_Head
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mathsflyinginsectbee
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could someone explain how to answer the circle question please

 

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Zeeshan Ahmed
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@mathsflyinginsectbee

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